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Chapter 19 Electrochemistry

In oxidation–reduction (redox) reactions, electrons are transferred from one species

(the reductant) to another (the oxidant). This transfer of electrons provides a means for

converting chemical energy to electrical energy or vice versa. The study of the

relationship between electricity and chemical reactions is called electrochemistry. In

this chapter, we describe electrochemical reactions in more depth and explore some of

their applications.

In the first three sections, we review redox reactions; describe how they can be used to

generate an electrical potential, or voltage; and discuss factors that affect the

magnitude of the potential. We then explore the relationships among the electrical

potential, the change in free energy, and the equilibrium constant for a redox reaction,

which are all measures of the thermodynamic driving force for a reaction. Finally, we

examine two kinds of applications of electrochemical principles: (1) those in which a

spontaneous reaction is used to provide electricity and (2) those in which electrical

energy is used to drive a thermodynamically nonspontaneous reaction. By the end of

this chapter, you will understand why different kinds of batteries are used in cars,

flashlights, cameras, and portable computers; how rechargeable batteries operate; and

why corrosion occurs and how to slow—if not prevent—it. You will also discover how

metal objects can be plated with silver or chromium for protection; how silver polish

removes tarnish; and how to calculate the amount of electricity needed to produce

aluminum, chlorine, copper, and sodium on an industrial scale.

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A view from the top of the Statue of Liberty, showing the green patina coating the

statue. The patina is formed by corrosion of the copper skin of the statue, which forms

a thin layer of an insoluble compound that contains copper(II), sulfate, and hydroxide

ions.

19.1 Describing Electrochemical Cells

Learning Objective

1. To distinguish between galvanic and electrolytic cells.

In any electrochemical process, electrons flow from one chemical substance to

another, driven by an oxidation–reduction (redox) reaction. As we described, a redox

reaction occurs when electrons are transferred from a substance that is oxidized to

one that is being reduced. The reductant is the substance that loses electrons and is

oxidized in the process; the oxidant is the species that gains electrons and is reduced



in the process. The associated potential energy is determined by the potential

difference between the valence electrons in atoms of different elements.

Because it is impossible to have a reduction without an oxidation and vice versa, a

redox reaction can be described as two half-reactions, one representing the oxidation

process and one the reduction process. For the reaction of zinc with bromine, the

overall chemical reaction is as follows:

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The half-reactions are as follows:



Each half-reaction is written to show what is actually occurring in the system; Zn is the

reductant in this reaction (it loses electrons), and Br2 is the oxidant (it gains electrons).

Adding the two half-reactions gives the overall chemical reaction. A redox reaction is

balanced when the number of electrons lost by the reductant equals the number of

electrons gained by the oxidant. Like any balanced chemical equation, the overall

process is electrically neutral; that is, the net charge is the same on both sides of the

equation.

Note the Pattern




In any redox reaction, the number of electrons lost by the reductant equals the number

of electrons gained by the oxidant.

In most of our discussions of chemical reactions, we have assumed that the reactants

are in intimate physical contact with one another. Acid–base reactions, for example,

are usually carried out with the acid and the base dispersed in a single phase, such as

a liquid solution. With redox reactions, however, it is possible to physically separate

the oxidation and reduction half-reactions in space, as long as there is a complete

circuit, including an external electrical connection, such as a wire, between the two

half-reactions. As the reaction progresses, the electrons flow from the reductant to the

oxidant over this electrical connection, producing an electric current that can be used

to do work. An apparatus that is used to generate electricity from a spontaneous redox

reaction or, conversely, that uses electricity to drive a nonspontaneous redox reaction

is called an electrochemical cell.

There are two types of electrochemical cells: galvanic cells and electrolytic cells. A

galvanic (voltaic) cellGalvanic cells are named for the Italian physicist and physician

Luigi Galvani (1737–1798), who observed that dissected frog leg muscles twitched

when a small electric shock was applied, demonstrating the electrical nature of nerve

impulses. uses the energy released during a spontaneous redox reaction (ΔG < 0) to

generate electricity. This type of electrochemical cell is often called a voltaic cell after

its inventor, the Italian physicist Alessandro Volta (1745–1827). In contrast, an

electrolytic cell consumes electrical energy from an external source, using it to cause a

nonspontaneous redox reaction to occur (ΔG > 0). Both types contain two electrodes,

which are solid metals connected to an external circuit that provides an electrical

connection between the two parts of the system (Figure below). The oxidation half-

reaction occurs at one electrode (the anode), and the reduction half-reaction occurs at

the other (the cathode). When the circuit is closed, electrons flow from the anode to

the cathode. The electrodes are also connected by an electrolyte, an ionic substance or

solution that allows ions to transfer between the electrode compartments, thereby

maintaining the system’s electrical neutrality. In this section, we focus on reactions

that occur in galvanic cells.

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Figure: Electrochemical Cells: A galvanic cell (left) transforms the energy released by

a spontaneous redox reaction into electrical energy that can be used to perform work.

The oxidative and reductive half-reactions usually occur in separate compartments that

are connected by an external electrical circuit; in addition, a second connection that

allows ions to flow between the compartments (shown here as a vertical dashed line to

represent a porous barrier) is necessary to maintain electrical neutrality. The potential

difference between the electrodes (voltage) causes electrons to flow from the

reductant to the oxidant through the external circuit, generating an electric current. In

an electrolytic cell (right), an external source of electrical energy is used to generate a

potential difference between the electrodes that forces electrons to flow, driving a

nonspontaneous redox reaction; only a single compartment is employed in most

applications. In both kinds of electrochemical cells, the anode is the electrode at which



the oxidation half-reaction occurs, and the cathode is the electrode at which the

reduction half-reaction occurs.

Galvanic (Voltaic) Cells

To illustrate the basic principles of a galvanic cell, let’s consider the reaction of

metallic zinc with cupric ion (Cu2+) to give copper metal and Zn2+ ion. The balanced

chemical equation is as follows:


We can cause this reaction to occur by inserting a zinc rod into an aqueous solution of

copper(II) sulfate. As the reaction proceeds, the zinc rod dissolves, and a mass of

metallic copper forms. These changes occur spontaneously, but all the energy released

is in the form of heat rather than in a form that can be used to do work.

This same reaction can be carried out using the galvanic cell illustrated in part (a) in

the Figure below. To assemble the cell, a copper strip is inserted into a beaker that

contains a 1 M solution of Cu2+ ions, and a zinc strip is inserted into a different beaker

that contains a 1 M solution of Zn2+ ions. The two metal strips, which serve as

electrodes, are connected by a wire, and the compartments are connected by a salt

bridge, a U-shaped tube inserted into both solutions that contains a concentrated

liquid or gelled electrolyte. The ions in the salt bridge are selected so that they do not

interfere with the electrochemical reaction by being oxidized or reduced themselves or

by forming a precipitate or complex; commonly used cations and anions are Na+ or K+

and NO3− or SO4

2−, respectively. (The ions in the salt bridge do not have to be the same

as those in the redox couple in either compartment.) When the circuit is closed, a

spontaneous reaction occurs: zinc metal is oxidized to Zn2+ ions at the zinc electrode

(the anode), and Cu2+ ions are reduced to Cu metal at the copper electrode (the


cathode). As the reaction progresses, the zinc strip dissolves, and the concentration of

Zn2+ ions in the Zn2+ solution increases; simultaneously, the copper strip gains mass,

and the concentration of Cu2+ ions in the Cu2+ solution decreases (part (b) in the Figure

below). Thus we have carried out the same reaction as we did using a single beaker,

but this time the oxidative and reductive half-reactions are physically separated from

each other. The electrons that are released at the anode flow through the wire,

producing an electric current. Galvanic cells therefore transform chemical energy into

electrical energy that can then be used to do work.

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Figure: The Reaction of Metallic Zinc with Aqueous Copper(II) Ions in a Galvanic Cell:

(a) A galvanic cell can be constructed by inserting a copper strip into a beaker that

contains an aqueous 1 M solution of Cu2+ ions and a zinc strip into a different beaker

that contains an aqueous 1 M solution of Zn2+ ions. The two metal strips are connected

by a wire that allows electricity to flow, and the beakers are connected by a salt

bridge. When the switch is closed to complete the circuit, the zinc electrode (the

anode) is spontaneously oxidized to Zn2+ ions in the left compartment, while Cu2+ ions

are simultaneously reduced to copper metal at the copper electrode (the cathode). (b)



As the reaction progresses, the Zn anode loses mass as it dissolves to give Zn2+(aq)

ions, while the Cu cathode gains mass as Cu2+(aq) ions are reduced to copper metal

that is deposited on the cathode.

The electrolyte in the salt bridge serves two purposes: it completes the circuit by

carrying electrical charge and maintains electrical neutrality in both solutions by

allowing ions to migrate between them. The identity of the salt in a salt bridge is

unimportant, as long as the component ions do not react or undergo a redox reaction

under the operating conditions of the cell. Without such a connection, the total positive

charge in the Zn2+ solution would increase as the zinc metal dissolves, and the total

positive charge in the Cu2+ solution would decrease. The salt bridge allows charges to

be neutralized by a flow of anions into the Zn2+ solution and a flow of cations into the

Cu2+ solution. In the absence of a salt bridge or some other similar connection, the

reaction would rapidly cease because electrical neutrality could not be maintained.

A voltmeter can be used to measure the difference in electrical potential between the

two compartments. Opening the switch that connects the wires to the anode and the

cathode prevents a current from flowing, so no chemical reaction occurs. With the

switch closed, however, the external circuit is closed, and an electric current can flow

from the anode to the cathode. The potential (Ecell) of the cell, measured in volts, is the

difference in electrical potential between the two half-reactions and is related to the

energy needed to move a charged particle in an electric field. In the cell we have

described, the voltmeter indicates a potential of 1.10 V (part (a) in the Figure above).

Because electrons from the oxidation half-reaction are released at the anode, the

anode in a galvanic cell is negatively charged. The cathode, which attracts electrons, is

positively charged.

Not all electrodes undergo a chemical transformation during a redox reaction. The

electrode can be made from an inert, highly conducting metal such as platinum to

prevent it from reacting during a redox process, where it does not appear in the

overall electrochemical reaction.

Note the Pattern

A galvanic (voltaic) cell converts the energy released by a spontaneous chemical

reaction to electrical energy. An electrolytic cell consumes electrical energy from an

external source to drive a nonspontaneous chemical reaction.

Constructing a Cell Diagram

Because it is somewhat cumbersome to describe any given galvanic cell in words, a

more convenient notation has been developed. In this line notation, called a cell

diagram, the identity of the electrodes and the chemical contents of the compartments

are indicated by their chemical formulas, with the anode written on the far left and the

cathode on the far right. Phase boundaries are shown by single vertical lines, and the

salt bridge, which has two phase boundaries, by a double vertical line. Thus the cell

diagram for the Zn/Cu cell shown in part (a) in the Figure above is written as follows:

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Figure

A cell diagram includes solution concentrations when they are provided.

Galvanic cells can have arrangements other than the examples we have seen so far.

For example, the voltage produced by a redox reaction can be measured more

accurately using two electrodes immersed in a single beaker containing an electrolyte



that completes the circuit. This arrangement reduces errors caused by resistance to

the flow of charge at a boundary, called the junction potential. One example of this

type of galvanic cell is as follows:


This cell diagram does not include a double vertical line representing a salt bridge

because there is no salt bridge providing a junction between two dissimilar solutions.

Moreover, solution concentrations have not been specified, so they are not included in

the cell diagram. The half-reactions and the overall reaction for this cell are as follows:




A single-compartment galvanic cell will initially exhibit the same voltage as a galvanic

cell constructed using separate compartments, but it will discharge rapidly because of

the direct reaction of the reactant at the anode with the oxidized member of the

cathodic redox couple. Consequently, cells of this type are not particularly useful for

producing electricity.





Summary

Electrochemistry is the study of the relationship between electricity and chemical

reactions. The oxidation–reduction reaction that occurs during an electrochemical

process consists of two half-reactions, one representing the oxidation process and one

the reduction process. The sum of the half-reactions gives the overall chemical

reaction. The overall redox reaction is balanced when the number of electrons lost by

the reductant equals the number of electrons gained by the oxidant. An electric

current is produced from the flow of electrons from the reductant to the oxidant. An

electrochemical cell can either generate electricity from a spontaneous redox reaction

or consume electricity to drive a nonspontaneous reaction. In a galvanic (voltaic) cell,

the energy from a spontaneous reaction generates electricity, whereas in an

electrolytic cell, electrical energy is consumed to drive a nonspontaneous redox

reaction. Both types of cells use two electrodes that provide an electrical connection

between systems that are separated in space. The oxidative half-reaction occurs at the

anode, and the reductive half-reaction occurs at the cathode. A salt bridge connects

the separated solutions, allowing ions to migrate to either solution to ensure the

system’s electrical neutrality. A voltmeter is a device that measures the flow of electric

current between two half-reactions. The potential of a cell, measured in volts, is the

energy needed to move a charged particle in an electric field. An electrochemical cell

can be described using line notation called a cell diagram, in which vertical lines

indicate phase boundaries and the location of the salt bridge. Resistance to the flow of

charge at a boundary is called the junction potential.

Key Takeaway

A galvanic (voltaic) cell uses the energy released during a spontaneous redox

reaction to generate electricity, whereas an electrolytic cell consumes electrical

energy from an external source to force a reaction to occur.

19.2 Standard Potentials

Learning Objectives

1. To use redox potentials to predict whether a reaction is spontaneous.

2. To balance redox reactions using half-reactions.

In a galvanic cell, current is produced when electrons flow externally through the

circuit from the anode to the cathode because of a difference in potential energy

between the two electrodes in the electrochemical cell. In the Zn/Cu system, the

valence electrons in zinc have a substantially higher potential energy than the valence

electrons in copper because of shielding of the s electrons of zinc by the electrons in

filled d orbitals. Hence electrons flow spontaneously from zinc to copper(II) ions,

forming zinc(II) ions and metallic copper (Figure below). Just like water flowing

spontaneously downhill, which can be made to do work by forcing a waterwheel, the

flow of electrons from a higher potential energy to a lower one can also be harnessed

to perform work.

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Figure: Potential Energy Difference in the Zn/Cu System: The potential energy of a

system consisting of metallic Zn and aqueous Cu2+ ions is greater than the potential

energy of a system consisting of metallic Cu and aqueous Zn2+ ions. Much of this

potential energy difference is because the valence electrons of metallic Zn are higher

in energy than the valence electrons of metallic Cu. Because the Zn(s) + Cu2+(aq)

system is higher in energy by 1.10 V than the Cu(s) + Zn2+(aq) system, energy is

released when electrons are transferred from Zn to Cu2+ to form Cu and Zn2+.

Because the potential energy of valence electrons differs greatly from one substance to

another, the voltage of a galvanic cell depends partly on the identity of the reacting

substances. If we construct a galvanic cell similar to the one in part (a) in Figure: "The

Reaction of Metallic Zinc with Aqueous Copper(II) Ions in a Galvanic Cell" but instead

of copper use a strip of cobalt metal and 1 M Co2+ in the cathode compartment, the

measured voltage is not 1.10 V but 0.51 V. Thus we can conclude that the difference in



potential energy between the valence electrons of cobalt and zinc is less than the

difference between the valence electrons of copper and zinc by 0.59 V.

The measured potential of a cell also depends strongly on the concentrations of the

reacting species and the temperature of the system. To develop a scale of relative

potentials that will allow us to predict the direction of an electrochemical reaction and

the magnitude of the driving force for the reaction, the potentials for oxidations and

reductions of different substances must be measured under comparable conditions. To

do this, chemists use the standard cell potential (E°cell), defined as the potential of a

cell measured under standard conditions—that is, with all species in their standard

states (1 M for solutions,Concentrated solutions of salts (about 1 M) generally do not

exhibit ideal behavior, and the actual standard state corresponds to an activity of 1

rather than a concentration of 1 M. Corrections for nonideal behavior are important for

precise quantitative work but not for the more qualitative approach that we are taking

here. 1 atm for gases, pure solids or pure liquids for other substances) and at a fixed

temperature, usually 25°C.

Note the Pattern

Measured redox potentials depend on the potential energy of valence electrons, the

concentrations of the species in the reaction, and the temperature of the system.

Measuring Standard Electrode Potentials

It is physically impossible to measure the potential of a single electrode: only the

difference between the potentials of two electrodes can be measured. (This is

analogous to measuring absolute enthalpies or free energies. Recall that only

differences in enthalpy and free energy can be measured.) We can, however, compare

the standard cell potentials for two different galvanic cells that have one kind of

electrode in common. This allows us to measure the potential difference between two

dissimilar electrodes. For example, the measured standard cell potential (E°) for the

Zn/Cu system is 1.10 V, whereas E° for the corresponding Zn/Co system is 0.51 V. This

implies that the potential difference between the Co and Cu electrodes is 1.10 V − 0.51

V = 0.59 V. In fact, that is exactly the potential measured under standard conditions if

a cell is constructed with the following cell diagram:


This cell diagram corresponds to the oxidation of a cobalt anode and the reduction of

Cu2+ in solution at the copper cathode.

All tabulated values of standard electrode potentials by convention are listed for a

reaction written as a reduction, not as an oxidation, to be able to compare standard

potentials for different substances. The standard cell potential (E°cell) is therefore the

difference between the tabulated reduction potentials of the two half-reactions, not

their sum:


In contrast, recall that half-reactions are written to show the reduction and oxidation

reactions that actually occur in the cell, so the overall cell reaction is written as the

sum of the two half-reactions. According to the Equation above, when we know the

standard potential for any single half-reaction, we can obtain the value of the standard

potential of many other half-reactions by measuring the standard potential of the

corresponding cell.

Note the Pattern



The overall cell reaction is the sum of the two half-reactions, but the cell potential is

the difference between the reduction potentials: E°cell = E°cathode − E°anode.

Although it is impossible to measure the potential of any electrode directly, we can

choose a reference electrode whose potential is defined as 0 V under standard

conditions. The standard hydrogen electrode (SHE) is universally used for this purpose

and is assigned a standard potential of 0 V. It consists of a strip of platinum wire in

contact with an aqueous solution containing 1 M H+. The [H+] in solution is in

equilibrium with H2 gas at a pressure of 1 atm at the Pt-solution interface (Figure

below). Protons are reduced or hydrogen molecules are oxidized at the Pt surface

according to the following equation:


One especially attractive feature of the SHE is that the Pt metal electrode is not

consumed during the reaction.


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Figure: The Standard Hydrogen Electrode: The SHE consists of platinum wire that is

connected to a Pt surface in contact with an aqueous solution containing 1 M H+ in

equilibrium with H2 gas at a pressure of 1 atm. In the molecular view, the Pt surface

catalyzes the oxidation of hydrogen molecules to protons or the reduction of protons to

hydrogen gas. (Water is omitted for clarity.) The standard potential of the SHE is

arbitrarily assigned a value of 0 V.

The Figure below shows a galvanic cell that consists of a SHE in one beaker and a Zn

strip in another beaker containing a solution of Zn2+ ions. When the circuit is closed,

the voltmeter indicates a potential of 0.76 V. The zinc electrode begins to dissolve to

form Zn2+, and H+ ions are reduced to H2 in the other compartment. Thus the hydrogen

electrode is the cathode, and the zinc electrode is the anode. The diagram for this

galvanic cell is as follows:




The half-reactions that actually occur in the cell and their corresponding electrode

potentials are as follows:




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Figure: Determining a Standard Electrode Potential Using a Standard Hydrogen

Electrode: The voltmeter shows that the standard cell potential of a galvanic cell

consisting of a SHE and a Zn/Zn2+ couple is E°cell = 0.76 V. Because the zinc electrode

in this cell dissolves spontaneously to form Zn2+(aq) ions while H+(aq) ions are reduced

to H2 at the platinum surface, the standard electrode potential of the Zn2+/Zn couple is

−0.76 V.

Although the reaction at the anode is an oxidation, by convention its tabulated E° value

is reported as a reduction potential. The potential of a half-reaction measured against

the SHE under standard conditions is called the standard electrode potential for that

half-reaction.In this example, the standard reduction potential for Zn2+(aq) + 2e− →

Zn(s) is −0.76 V, which means that the standard electrode potential for the reaction

that occurs at the anode, the oxidation of Zn to Zn2+, often called the Zn/Zn2+ redox

couple, or the Zn/Zn2+ couple, is −(−0.76 V) = 0.76 V. We must therefore subtract

E°anode from E°cathode to obtain E°cell: 0 − (−0.76 V) = 0.76 V.

Because electrical potential is the energy needed to move a charged particle in an

electric field, standard electrode potentials for half-reactions are intensive properties

and do not depend on the amount of substance involved. Consequently, E° values are

independent of the stoichiometric coefficients for the half-reaction, and, most

important, the coefficients used to produce a balanced overall reaction do not affect

the value of the cell potential.

Note the Pattern

E° values do not depend on the stoichiometric coefficients for a half-reaction.

To measure the potential of the Cu/Cu2+ couple, we can construct a galvanic cell

analogous to the one shown in the Figure above but containing a Cu/Cu2+ couple in the

sample compartment instead of Zn/Zn2+. When we close the circuit this time, the

measured potential for the cell is negative (−0.34 V) rather than positive. The negative

value of E°cell indicates that the direction of spontaneous electron flow is the opposite

of that for the Zn/Zn2+ couple. Hence the reactions that occur spontaneously, indicated

by a positive E°cell, are the reduction of Cu2+ to Cu at the copper electrode. The copper

electrode gains mass as the reaction proceeds, and H2 is oxidized to H+ at the platinum

electrode. In this cell, the copper strip is the cathode, and the hydrogen electrode is

the anode. The cell diagram therefore is written with the SHE on the left and the

Cu2+/Cu couple on the right:


The half-cell reactions and potentials of the spontaneous reaction are as follows:




Thus the standard electrode potential for the Cu2+/Cu couple is 0.34 V.

Balancing Redox Reactions Using the Half-Reaction Method





We have described a method for balancing redox reactions using oxidation numbers.

Oxidation numbers were assigned to each atom in a redox reaction to identify any

changes in the oxidation states. Here we present an alternative approach to balancing

redox reactions, the half-reaction method, in which the overall redox reaction is

divided into an oxidation half-reaction and a reduction half-reaction, each balanced for

mass and charge. This method more closely reflects the events that take place in an

electrochemical cell, where the two half-reactions may be physically separated from

each other.

We can illustrate how to balance a redox reaction using half-reactions with the

reaction that occurs when Drano, a commercial solid drain cleaner, is poured into a

clogged drain. Drano contains a mixture of sodium hydroxide and powdered aluminum,

which in solution reacts to produce hydrogen gas:


In this reaction, Al(s) is oxidized to Al3+, and H+ in water is reduced to H2 gas, which

bubbles through the solution, agitating it and breaking up the clogs.

The overall redox reaction is composed of a reduction half-reaction and an oxidation

half-reaction. From the standard electrode potentials listed, we find the corresponding

half-reactions that describe the reduction of H+ ions in water to H2 and the oxidation of

Al to Al3+ in basic solution:





The half-reactions chosen must exactly reflect the reaction conditions, such as the

basic conditions shown here. Moreover, the physical states of the reactants and the

products must be identical to those given in the overall reaction, whether gaseous,

liquid, solid, or in solution.

In the second to last Equation above, two H+ ions gain one electron each in the

reduction; in the Equation above, the aluminum atom loses three electrons in the

oxidation. The charges are balanced by multiplying the reduction half-reaction by 3

and the oxidation half-reaction by 2 to give the same number of electrons in both half-

reactions:



Adding the two half-reactions,


Simplifying by canceling substances that appear on both sides of the equation,






We have a −2 charge on the left side of the equation and a −2 charge on the right side.

Thus the charges are balanced, but we must also check that atoms are balanced:


The atoms also balance, so the second to last Equation above is a balanced chemical

equation for the redox reaction depicted in one of the previous Equations.

Note the Pattern

The half-reaction method requires that half-reactions exactly reflect reaction

conditions, and the physical states of the reactants and the products must be identical

to those in the overall reaction.

We can also balance a redox reaction by first balancing the atoms in each half-reaction

and then balancing the charges. With this alternative method, we focus on the atoms

whose oxidation states change, as illustrated in the following steps:

Step 1: Write the reduction half-reaction and the oxidation half-reaction.

For the reaction shown in one of the Equations above, hydrogen is reduced from H+ in

OH− to H2, and aluminum is oxidized from Al0 to Al3+:






Step 2: Balance the atoms by balancing elements other than O and H. Then balance O

atoms by adding H2O and balance H atoms by adding H+.

Elements other than O and H in the previous two equations are balanced as written, so

we proceed with balancing the O atoms. We can do this by adding water to the

appropriate side of each half-reaction:



Balancing H atoms by adding H+, we obtain the following:



We have now balanced the atoms in each half-reaction, but the charges are not

balanced.

Step 3: Balance the charges in each half-reaction by adding electrons.






Two electrons are gained in the reduction of H+ ions to H2, and three electrons are lost

during the oxidation of Al0 to Al3+:



Step 4: Multiply the reductive and oxidative half-reactions by appropriate integers to

obtain the same number of electrons in both half-reactions.

In this case, we multiply the second to last Equation above (the reductive half-reaction)

by 3 and the Equation above (the oxidative half-reaction) by 2 to obtain the same

number of electrons in both half-reactions:



Step 5: Add the two half-reactions and cancel substances that appear on both sides of

the equation.

Adding and, in this case, canceling 8H+, 3H2O, and 6e−,






We have three OH− and one H+ on the left side. Neutralizing the H+ gives us a total of

5H2O + H2O = 6H2O and leaves 2OH− on the left side:


Step 6: Check to make sure that all atoms and charges are balanced.

The Equation above is identical to one of the Equations above, obtained using the first

method, so the charges and numbers of atoms on each side of the equation balance.

Calculating Standard Cell Potentials

The standard cell potential for a redox reaction (E°cell) is a measure of the tendency of

reactants in their standard states to form products in their standard states;

consequently, it is a measure of the driving force for the reaction, which earlier we

called voltage. We can use the two standard electrode potentials we found earlier to

calculate the standard potential for the Zn/Cu cell represented by the following cell

diagram:


We know the values of E°anode for the reduction of Zn2+ and E°cathode for the reduction of

Cu2+, so we can calculate E°cell:







This is the same value that is observed experimentally. If the value of E°cell is positive,

the reaction will occur spontaneously as written. If the value of E°cell is negative, then

the reaction is not spontaneous, and it will not occur as written under standard

conditions; it will, however, proceed spontaneously in the opposite direction. As we

shall see, this does not mean that the reaction cannot be made to occur at all under

standard conditions. With a sufficient input of electrical energy, virtually any reaction

can be forced to occur. Example 4 and its corresponding exercise illustrate how we can

use measured cell potentials to calculate standard potentials for redox couples.

Note the Pattern

A positive E°cell means that the reaction will occur spontaneously as written. A negative

E°cell means that the reaction will proceed spontaneously in the opposite direction.

Reference Electrodes and Measuring Concentrations

When using a galvanic cell to measure the concentration of a substance, we are

generally interested in the potential of only one of the electrodes of the cell, the so-

called indicator electrode, whose potential is related to the concentration of the




substance being measured. To ensure that any change in the measured potential of the

cell is due to only the substance being analyzed, the potential of the other electrode,

the reference electrode, must be constant. You are already familiar with one example

of a reference electrode: the SHE. The potential of a reference electrode must be

unaffected by the properties of the solution, and if possible, it should be physically

isolated from the solution of interest. To measure the potential of a solution, we select

a reference electrode and an appropriate indicator electrode. Whether reduction or

oxidation of the substance being analyzed occurs depends on the potential of the half-

reaction for the substance of interest (the sample) and the potential of the reference

electrode.

Note the Pattern

The potential of any reference electrode should not be affected by the properties of the

solution to be analyzed, and it should also be physically isolated.

There are many possible choices of reference electrode other than the SHE. The SHE

requires a constant flow of highly flammable hydrogen gas, which makes it

inconvenient to use. Consequently, two other electrodes are commonly chosen as

reference electrodes. One is the silver–silver chloride electrode, which consists of a

silver wire coated with a very thin layer of AgCl that is dipped into a chloride ion

solution with a fixed concentration. The cell diagram and reduction half-reaction are as

follows:


If a saturated solution of KCl is used as the chloride solution, the potential of the

silver–silver chloride electrode is 0.197 V versus the SHE. That is, 0.197 V must be


subtracted from the measured value to obtain the standard electrode potential

measured against the SHE.

A second common reference electrode is the saturated calomel electrode (SCE), which

has the same general form as the silver–silver chloride electrode. The SCE consists of a

platinum wire inserted into a moist paste of liquid mercury (Hg2Cl2; called calomel in

the old chemical literature) and KCl. This interior cell is surrounded by an aqueous KCl

solution, which acts as a salt bridge between the interior cell and the exterior solution

(part (a) in the Figure below). Although it sounds and looks complex, this cell is

actually easy to prepare and maintain, and its potential is highly reproducible. The

SCE cell diagram and corresponding half-reaction are as follows:



http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0m/section_23/502acee270b6333872101f77e2093437.jpg

Figure: Three Common Types of Electrodes: (a) The SCE is a reference electrode that

consists of a platinum wire inserted into a moist paste of liquid mercury (calomel;

Hg2Cl2) and KCl. The interior cell is surrounded by an aqueous KCl solution, which acts

as a salt bridge between the interior cell and the exterior solution. (b) In a glass





electrode, an internal Ag/AgCl electrode is immersed in a 1 M HCl solution that is

separated from the sample solution by a very thin glass membrane. The potential of

the electrode depends on the H+ ion concentration of the sample. (c) The potential of

an ion-selective electrode depends on the concentration of only a single ionic species

in solution.

At 25°C, the potential of the SCE is 0.2415 V versus the SHE, which means that 0.2415

V must be subtracted from the potential versus an SCE to obtain the standard

electrode potential.

One of the most common uses of electrochemistry is to measure the H+ ion

concentration of a solution. A glass electrode is generally used for this purpose, in

which an internal Ag/AgCl electrode is immersed in a 0.10 M HCl solution that is

separated from the solution by a very thin glass membrane (part (b) in the Figure

above). The glass membrane absorbs protons, which affects the measured potential.

The extent of the adsorption on the inner side is fixed because [H+] is fixed inside the

electrode, but the adsorption of protons on the outer surface depends on the pH of the

solution. The potential of the glass electrode depends on [H+] as follows (recall that pH

= −log[H+]:


The voltage E′ is a constant that depends on the exact construction of the electrode.

Although it can be measured, in practice, a glass electrode is calibrated; that is, it is

inserted into a solution of known pH, and the display on the pH meter is adjusted to

the known value. Once the electrode is properly calibrated, it can be placed in a

solution and used to determine an unknown pH.


Ion-selective electrodes are used to measure the concentration of a particular species

in solution; they are designed so that their potential depends on only the concentration

of the desired species (part (c) in the Figure above). These electrodes usually contain

an internal reference electrode that is connected by a solution of an electrolyte to a

crystalline inorganic material or a membrane, which acts as the sensor. For example,

one type of ion-selective electrode uses a single crystal of Eu-doped LaF3 as the

inorganic material. When fluoride ions in solution diffuse to the surface of the solid, the

potential of the electrode changes, resulting in a so-called fluoride electrode. Similar

electrodes are used to measure the concentrations of other species in solution. Some

of the species whose concentrations can be determined in aqueous solution using ion-

selective electrodes and similar devices are listed in the Table below.

Species Type of Sample

H+ laboratory samples, blood, soil, and ground and surface water

NH3/NH4+ wastewater and runoff water

K+ blood, wine, and soil

CO2/HCO3− blood and groundwater

F− groundwater, drinking water, and soil

Br− grains and plant extracts

I− milk and pharmaceuticals

NO3− groundwater, drinking water, soil, and fertilizer

Table: Some Species Whose Aqueous Concentrations Can Be Measured Using

Electrochemical Methods

Summary

The flow of electrons in an electrochemical cell depends on the identity of the reacting

substances, the difference in the potential energy of their valence electrons, and their

concentrations. The potential of the cell under standard conditions (1 M for solutions,

1 atm for gases, pure solids or liquids for other substances) and at a fixed temperature

(25°C) is called the standard cell potential (E°cell). Only the difference between the

potentials of two electrodes can be measured. By convention, all tabulated values of

standard electrode potentials are listed as standard reduction potentials. The overall

cell potential is the reduction potential of the reductive half-reaction minus the

reduction potential of the oxidative half-reaction (E°cell = E°cathode − E°anode). The

potential of the standard hydrogen electrode (SHE) is defined as 0 V under standard

conditions. The potential of a half-reaction measured against the SHE under standard

conditions is called its standard electrode potential. The standard cell potential is a

measure of the driving force for a given redox reaction. All E° values are independent

of the stoichiometric coefficients for the half-reaction. Redox reactions can be balanced

using the half-reaction method, in which the overall redox reaction is divided into an

oxidation half-reaction and a reduction half-reaction, each balanced for mass and

charge. The half-reactions selected from tabulated lists must exactly reflect reaction

conditions. In an alternative method, the atoms in each half-reaction are balanced, and

then the charges are balanced. Whenever a half-reaction is reversed, the sign of E°

corresponding to that reaction must also be reversed. If E°cell is positive, the reaction

will occur spontaneously under standard conditions. If E°cell is negative, then the

reaction is not spontaneous under standard conditions, although it will proceed

spontaneously in the opposite direction. The potential of an indicator electrode is

related to the concentration of the substance being measured, whereas the potential of

the reference electrode is held constant. Whether reduction or oxidation occurs

depends on the potential of the sample versus the potential of the reference electrode.

In addition to the SHE, other reference electrodes are the silver–silver chloride

electrode; the saturated calomel electrode (SCE); the glass electrode, which is

commonly used to measure pH; and ion-selective electrodes, which depend on the

concentration of a single ionic species in solution. Differences in potential between the

SHE and other reference electrodes must be included when calculating values for E°.

Key Takeaways

Redox reactions can be balanced using the half-reaction method.

The standard cell potential is a measure of the driving force for the reaction.

Key Equation

Standard cell potential

19.3 Comparing Strengths of Oxidants and Reductants

Learning Objective

1. To know how to predict the relative strengths of various oxidants and

reductants.

We can use the procedure described to measure the standard potentials for a wide

variety of chemical substances, some of which are listed in the Table below. These data

allow us to compare the oxidative and reductive strengths of a variety of substances.

The half-reaction for the standard hydrogen electrode (SHE) lies more than halfway

down the list in the Table below. All reactants that lie above the SHE in the table are

stronger oxidants than H+, and all those that lie below the SHE are weaker. The

strongest oxidant in the table is F2, with a standard electrode potential of 2.87 V. This

high value is consistent with the high electronegativity of fluorine and tells us that

fluorine has a stronger tendency to accept electrons (it is a stronger oxidant) than any

other element.

Half-Reaction E° (V)

F2(g) + 2e−→ 2F−(aq) 2.87

H2O2(aq) + 2H+(aq) + 2e− → 2H2O(l) 1.78


Ce4+(aq) + e− → Ce3+(aq) 1.72

PbO2(s) + HSO4−(aq) + 3H+(aq) + 2e− → PbSO4(s) + 2H2O(l) 1.69

Cl2(g) + 2e− → 2Cl−(aq) 1.36

Cr2O72−(aq) + 14H+(aq) + 6e− → 2Cr3+(aq) + 7H2O(l) 1.23

O2(g) + 4H+(aq) + 4e− → 2H2O(l) 1.23

MnO2(s) + 4H+(aq) + 2e− → Mn2+(aq) + 2H2O(l) 1.22

Br2(aq) + 2e− → 2Br−(aq) 1.09

NO3−(aq) + 3H+(aq) + 2e− → HNO2(aq) + H2O(l) 0.93

Ag+(aq) + e− → Ag(s) 0.80

Fe3+(aq) + e− → Fe2+(aq) 0.77

H2SeO3(aq) + 4H+ + 4e− → Se(s) + 3H2O(l) 0.74

O2(g) + 2H+(aq) + 2e− → H2O2(aq) 0.70

MnO4−(aq) + 2H2O(l) + 3e− → MnO2(s) + 4OH−(aq) 0.60

MnO42−(aq) + 2H2O(l) + 2e− → MnO2(s) + 4OH−(aq) 0.60

I2(s) + 2e− → 2I−(aq) 0.54

H2SO3(aq) + 4H+(aq) + 4e− → S(s) + 3H2O(l) 0.45

O2(g) + 2H2O(l) + 4e− → 4OH−(aq) 0.40

Cu2+(aq) + 2e− → Cu(s) 0.34

AgCl(s) + e− → Ag(s) + Cl−(aq) 0.22

Cu2+(aq) + e− → Cu+(aq) 0.15

Sn4+(aq) + 2e− → Sn2+(aq) 0.15

2H+(aq) + 2e− → H2(g) 0.00

Sn2+(aq) + 2e− → Sn(s) −0.14

2SO42−(aq) + 4H+(aq) + 2e− → S2O6

2−(aq) + 2H2O(l) −0.22

Ni2+(aq) + 2e− → Ni(s) −0.26

PbSO4(s) + 2e− → Pb(s) + SO42−(aq) −0.36

Cd2+(aq) + 2e− → Cd(s) −0.40

Cr3+(aq) + e− → Cr2+(aq) −0.41


Fe2+(aq) + 2e− → Fe(s) −0.45

Ag2S(s) + 2e− → 2Ag(s) + S2−(aq) −0.69

Zn2+(aq) + 2e− → Zn(s) −0.76

Al3+(aq) + 3e− → Al(s) −1.662

Be2+(aq) + 2e− → Be(s) −1.85

Li+(aq) + e− → Li(s) −3.04

Table: Standard Potentials for Selected Reduction Half-Reactions at 25°C

Similarly, all species in the Table above that lie below H2 are stronger reductants than

H2, and those that lie above H2 are weaker. The strongest reductant in the table is thus

metallic lithium, with a standard electrode potential of −3.04 V. This fact might be

surprising because cesium, not lithium, is the least electronegative element. The

apparent anomaly can be explained by the fact that electrode potentials are measured

in aqueous solution, where intermolecular interactions are important, whereas

ionization potentials and electron affinities are measured in the gas phase. Due to its

small size, the Li+ ion is stabilized in aqueous solution by strong electrostatic

interactions with the negative dipole end of water molecules. These interactions result

in a significantly greater ΔHhydration for Li+ compared with Cs+. Lithium metal is

therefore the strongest reductant (most easily oxidized) of the alkali metals in aqueous

solution.

Note the Pattern

Species in the Table above that lie below H2 are stronger reductants (more easily

oxidized) than H2. Species that lie above H2 are stronger oxidants.

Because the half-reactions shown in the Table above are arranged in order of their E°

values, we can use the table to quickly predict the relative strengths of various

oxidants and reductants. Any species on the left side of a half-reaction will

spontaneously oxidize any species on the right side of another half-reaction that lies

below it in the table. Conversely, any species on the right side of a half-reaction will

spontaneously reduce any species on the left side of another half-reaction that lies

above it in the table. We can use these generalizations to predict the spontaneity of a

wide variety of redox reactions (E°cell > 0), as illustrated in Example 5.

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Although the sign of E°cell tells us whether a particular redox reaction will occur

spontaneously under standard conditions, it does not tell us to what extent the reaction

proceeds, and it does not tell us what will happen under nonstandard conditions. To

answer these questions requires a more quantitative understanding of the relationship

between electrochemical cell potential and chemical thermodynamics.

Summary

The oxidative and reductive strengths of a variety of substances can be compared

using standard electrode potentials. Apparent anomalies can be explained by the fact

that electrode potentials are measured in aqueous solution, which allows for strong

intermolecular electrostatic interactions, and not in the gas phase.



Key Takeaway

The relative strengths of various oxidants and reductants can be predicted using

E° values.

19.4 Electrochemical Cells and Thermodynamics

Learning Objectives

1. To understand the relationship between cell potential and the equilibrium

constant.

2. To use cell potentials to calculate solution concentrations.

Changes in reaction conditions can have a tremendous effect on the course of a redox

reaction. For example, under standard conditions, the reaction of Co(s) with Ni2+(aq) to

form Ni(s) and Co2+(aq) occurs spontaneously, but if we reduce the concentration of

Ni2+ by a factor of 100, so that [Ni2+] is 0.01 M, then the reverse reaction occurs

spontaneously instead. The relationship between voltage and concentration is one of

the factors that must be understood to predict whether a reaction will be spontaneous.

The Relationship between Cell Potential and Free Energy

Electrochemical cells convert chemical energy to electrical energy and vice versa. The

total amount of energy produced by an electrochemical cell, and thus the amount of

energy available to do electrical work, depends on both the cell potential and the total

number of electrons that are transferred from the reductant to the oxidant during the

course of a reaction. The resulting electric current is measured in coulombs (C), an SI

unit that measures the number of electrons passing a given point in 1 s. A coulomb

relates energy (in joules) to electrical potential (in volts). Electric current is measured

in amperes (A); 1 A is defined as the flow of 1 C/s past a given point (1 C = 1 A·s):


In chemical reactions, however, we need to relate the coulomb to the charge on a mole

of electrons. Multiplying the charge on the electron by Avogadro’s number gives us the

charge on 1 mol of electrons, which is called the faraday (F), named after the English

physicist and chemist Michael Faraday (1791–1867):


The total charge transferred from the reductant to the oxidant is therefore nF, where n

is the number of moles of electrons.

Michael Faraday (1791–1867)

Faraday was a British physicist and chemist who was arguably one of the greatest

experimental scientists in history. The son of a blacksmith, Faraday was self-educated

and became an apprentice bookbinder at age 14 before turning to science. His

experiments in electricity and magnetism made electricity a routine tool in science and

led to both the electric motor and the electric generator. He discovered the

phenomenon of electrolysis and laid the foundations of electrochemistry. In fact, most

of the specialized terms introduced in this chapter (electrode, anode, cathode, and so

forth) are due to Faraday. In addition, he discovered benzene and invented the system

of oxidation state numbers that we use today. Faraday is probably best known for “The



Chemical History of a Candle,” a series of public lectures on the chemistry and physics

of flames.

The maximum amount of work that can be produced by an electrochemical cell (wmax) is

equal to the product of the cell potential (Ecell) and the total charge transferred during

the reaction (nF):


Work is expressed as a negative number because work is being done by a system (an

electrochemical cell with a positive potential) on its surroundings.

As you learned, the change in free energy (ΔG) is also a measure of the maximum

amount of work that can be performed during a chemical process (ΔG = wmax).

Consequently, there must be a relationship between the potential of an

electrochemical cell and ΔG, the most important thermodynamic quantity previously

discussed. This relationship is as follows:


A spontaneous redox reaction is therefore characterized by a negative value of ΔG and

a positive value of Ecell, consistent with our earlier discussions. When both reactants

and products are in their standard states, the relationship between ΔG° and E°cell is as

follows:





Note the Pattern

A spontaneous redox reaction is characterized by a negative value of ΔG°, which

corresponds to a positive value of E°cell.

Potentials for the Sums of Half-Reactions

Although Table: "Standard Potentials for Selected Reduction Half-Reactions at 25°C"

lists several half-reactions, many more are known. When the standard potential for a

half-reaction is not available, we can use relationships between standard potentials

and free energy to obtain the potential of any other half-reaction that can be written as

the sum of two or more half-reactions whose standard potentials are available. For

example, the potential for the reduction of Fe3+(aq) to Fe(s) is not listed in the table,

but two related reductions are given:



Although the sum of these two half-reactions gives the desired half-reaction, we cannot

simply add the potentials of two reductive half-reactions to obtain the potential of a

third reductive half-reaction because E° is not a state function. However, because ΔG°

is a state function, the sum of the ΔG° values for the individual reactions gives us ΔG°

for the overall reaction, which is proportional to both the potential and the number of

electrons (n) transferred. To obtain the value of E° for the overall half-reaction, we first

must add the values of ΔG° (= −nFE°) for each individual half-reaction to obtain ΔG°

for the overall half-reaction:




Solving the last expression for ΔG° for the overall half-reaction,


Three electrons (n = 3) are transferred in the overall reaction (second to last Equation

above), so substituting into the relationship between ΔG° and E°cell Equation and

solving for E° gives the following:


This value of E° is very different from the value that is obtained by simply adding the

potentials for the two half-reactions (0.32 V) and even has the opposite sign.

Note the Pattern

Values of E° for half-reactions cannot be added to give E° for the sum of the half-

reactions; only values of ΔG° = −nFE°cell for half-reactions can be added.

The Relationship between Cell Potential and the Equilibrium Constant




We can use the relationship between ΔG° and the equilibrium constant K, previously

defined, to obtain a relationship between E°cell and K. Recall that for a general reaction

of the type aA + bB → cC + dD, the standard free-energy change and the equilibrium

constant are related by the following equation:


Given the relationship between the standard free-energy change and the standard cell

potential, we can write


Rearranging this equation,


For T = 298 K, the Equation above can be simplified as follows:






Thus E°cell is directly proportional to the logarithm of the equilibrium constant. This

means that large equilibrium constants correspond to large positive values of E°cell and

vice versa.

The Figure below summarizes the relationships that we have developed based on

properties of the system—that is, based on the equilibrium constant, standard free-

energy change, and standard cell potential—and the criteria for spontaneity (ΔG° < 0).

Unfortunately, these criteria apply only to systems in which all reactants and products

are present in their standard states, a situation that is seldom encountered in the real

world. A more generally useful relationship between cell potential and reactant and

product concentrations, as we are about to see, uses the relationship between ΔG and

the reaction quotient Q developed.

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Figure: The Relationships among Criteria for Thermodynamic Spontaneity: The three

properties of a system that can be used to predict the spontaneity of a redox reaction

under standard conditions are K, ΔG°, and E°cell. If we know the value of one of these

quantities, then these relationships enable us to calculate the value of the other two.

The signs of ΔG° and E°cell and the magnitude of K determine the direction of

spontaneous reaction under standard conditions.

The Effect of Concentration on Cell Potential: The Nernst Equation



Recall that the actual free-energy change for a reaction under nonstandard conditions,

ΔG, is given as follows:


We also know that ΔG = −nFEcell and ΔG° = −nFE°cell. Substituting these expressions

into the Equation above, we obtain


Dividing both sides of this equation by −nF,


The cell diagram and reduction half-reaction Equation is called the Nernst equation,

after the German physicist and chemist Walter Nernst (1864–1941), who first derived

it. The Nernst equation is arguably the most important relationship in

electrochemistry. When a redox reaction is at equilibrium (ΔG = 0), the cell diagram

and reduction half-reaction reduces to one of the Equations above because Q = K, and

there is no net transfer of electrons (i.e., Ecell = 0).

Substituting the values of the constants into the cell diagram and reduction half-

reaction Equation with T = 298 K and converting to base-10 logarithms give the

relationship of the actual cell potential (Ecell), the standard cell potential (E°cell), and the

reactant and product concentrations at room temperature (contained in Q):





Note the Pattern

The Nernst equation can be used to determine the value of Ecell, and thus the direction

of spontaneous reaction, for any redox reaction under any conditions.

The Equation above allows us to calculate the potential associated with any

electrochemical cell at 298 K for any combination of reactant and product

concentrations under any conditions. We can therefore determine the spontaneous

direction of any redox reaction under any conditions, as long as we have tabulated

values for the relevant standard electrode potentials. Notice in the Equation above that

the cell potential changes by 0.0591/n V for each 10-fold change in the value of Q

because log 10 = 1.

Applying the Nernst equation to a simple electrochemical cell such as the Zn/Cu cell

previously discussed allows us to see how the cell voltage varies as the reaction

progresses and the concentrations of the dissolved ions change. Recall that the overall

reaction for this cell is as follows:


The reaction quotient is therefore Q = [Zn2+]/[Cu2+]. Suppose that the cell initially

contains 1.0 M Cu2+ and 1.0 × 10−6 M Zn2+. The initial voltage measured when the cell

is connected can then be calculated from the standard cell potential Equation:




Thus the initial voltage is greater than E° because Q < 1. As the reaction proceeds,

[Zn2+] in the anode compartment increases as the zinc electrode dissolves, while [Cu2+]

in the cathode compartment decreases as metallic copper is deposited on the

electrode. During this process, the ratio Q = [Zn2+]/[Cu2+] steadily increases, and the

cell voltage therefore steadily decreases. Eventually, [Zn2+] = [Cu2+], so Q = 1 and Ecell

= E°cell. Beyond this point, [Zn2+] will continue to increase in the anode compartment,

and [Cu2+] will continue to decrease in the cathode compartment. Thus the value of Q

will increase further, leading to a further decrease in Ecell. When the concentrations in

the two compartments are the opposite of the initial concentrations (i.e., 1.0 M Zn2+

and 1.0 × 10−6 M Cu2+), Q = 1.0 × 106, and the cell potential will be reduced to 0.92 V.

The variation of Ecell with log Q over this range is linear with a slope of −0.0591/n, as

illustrated in the Figure below. As the reaction proceeds still further, Q continues to

increase, and Ecell continues to decrease. If neither of the electrodes dissolves

completely, thereby breaking the electrical circuit, the cell voltage will eventually

reach zero. This is the situation that occurs when a battery is “dead.” The value of Q

when Ecell = 0 is calculated as follows:



http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0m/section_23/d5ecb74a29e2c5f208defc391be185e0.jpg

Figure: The Variation of E cell with Log Q for a Zn/Cu Cell : Initially, log Q < 0, and the

voltage of the cell is greater than E°cell. As the reaction progresses, log Q increases,

and Ecell decreases. When [Zn2+] = [Cu2+], log Q = 0 and Ecell = E°cell = 1.10 V. As long

as the electrical circuit remains intact, the reaction will continue, and log Q will

increase until Q = K and the cell voltage reaches zero. At this point, the system will

have reached equilibrium.

Recall that at equilibrium, Q = K. Thus the equilibrium constant for the reaction of Zn

metal with Cu2+ to give Cu metal and Zn2+ is 1.7 × 1037 at 25°C.




Concentration Cells

A voltage can also be generated by constructing an electrochemical cell in which each

compartment contains the same redox active solution but at different concentrations.

The voltage is produced as the concentrations equilibrate. Suppose, for example, we

have a cell with 0.010 M AgNO3 in one compartment and 1.0 M AgNO3 in the other.

The cell diagram and corresponding half-reactions are as follows:





As the reaction progresses, the concentration of Ag+ will increase in the left (oxidation)

compartment as the silver electrode dissolves, while the Ag+ concentration in the right

(reduction) compartment decreases as the electrode in that compartment gains mass.

The total mass of Ag(s) in the cell will remain constant, however. We can calculate the

potential of the cell using the Nernst equation, inserting 0 for E°cell because E°cathode =

−E°anode:





http://academic.csc.edu/oer/chem1/wp-content/uploads/2014/07/Cell-Potential-Calculation.png

An electrochemical cell of this type, in which the anode and cathode compartments are

identical except for the concentration of a reactant, is called a concentration cell. As

the reaction proceeds, the difference between the concentrations of Ag+ in the two

compartments will decrease, as will Ecell. Finally, when the concentration of Ag+ is the

same in both compartments, equilibrium will have been reached, and the measured

potential difference between the two compartments will be zero (Ecell = 0).

Using Cell Potentials to Measure Solubility Products

Because voltages are relatively easy to measure accurately using a voltmeter,

electrochemical methods provide a convenient way to determine the concentrations of

very dilute solutions and the solubility products (Ksp) of sparingly soluble substances.

As you learned, solubility products can be very small, with values of less than or equal

to 10−30. Equilibrium constants of this magnitude are virtually impossible to measure

accurately by direct methods, so we must use alternative methods that are more

sensitive, such as electrochemical methods.

To understand how an electrochemical cell is used to measure a solubility product,

consider the cell shown in the Figure below, which is designed to measure the

solubility product of silver chloride: Ksp = [Ag+][Cl−]. In one compartment, the cell

contains a silver wire inserted into a 1.0 M solution of Ag+; the other compartment

contains a silver wire inserted into a 1.0 M Cl− solution saturated with AgCl. In this

system, the Ag+ ion concentration in the first compartment equals Ksp. We can see this

by dividing both sides of the equation for Ksp by [Cl−] and substituting: [Ag+] = Ksp/[Cl−]

= Ksp/1.0 = Ksp. The overall cell reaction is as follows:

http://academic.csc.edu/oer/chem1/wp-content/uploads/2014/07/Cell-Potential-Calculation.png

Ag+(aq, concentrated) → Ag+(aq, dilute)

Thus the voltage of the concentration cell due to the difference in [Ag+] between the

two cells is as follows:


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Figure: A Galvanic Cell for Measuring the Solubility Product of AgCl: One

compartment contains a silver wire inserted into a 1.0 M solution of Ag+, and the other

compartment contains a silver wire inserted into a 1.0 M Cl− solution saturated with

AgCl. The potential due to the difference in [Ag+] between the two cells can be used to

determine Ksp.

By closing the circuit, we can measure the potential caused by the difference in [Ag+]

in the two cells. In this case, the experimentally measured voltage of the concentration

cell at 25°C is 0.580 V. Solving the Equation above for Ksp,





Thus a single potential measurement can provide the information we need to

determine the value of the solubility product of a sparingly soluble salt.

Summary

A coulomb (C) relates electrical potential, expressed in volts, and energy, expressed in

joules. The current generated from a redox reaction is measured in amperes (A), where

1 A is defined as the flow of 1 C/s past a given point. The faraday (F) is Avogadro’s

number multiplied by the charge on an electron and corresponds to the charge on 1

mol of electrons. The product of the cell potential and the total charge is the maximum

amount of energy available to do work, which is related to the change in free energy

that occurs during the chemical process. Adding together the ΔG values for the half-

reactions gives ΔG for the overall reaction, which is proportional to both the potential

and the number of electrons (n) transferred. Spontaneous redox reactions have a

negative ΔG and therefore a positive Ecell. Because the equilibrium constant K is related

to ΔG, E°cell and K are also related. Large equilibrium constants correspond to large

positive values of E°. The Nernst equation allows us to determine the spontaneous

direction of any redox reaction under any reaction conditions from values of the

relevant standard electrode potentials. Concentration cells consist of anode and

cathode compartments that are identical except for the concentrations of the reactant.

Because ΔG = 0 at equilibrium, the measured potential of a concentration cell is zero

at equilibrium (the concentrations are equal). A galvanic cell can also be used to

measure the solubility product of a sparingly soluble substance and calculate the


concentration of a species given a measured potential and the concentrations of all the

other species.

Key Takeaway

The Nernst equation can be used to determine the direction of spontaneous

reaction for any redox reaction in aqueous solution.

Key Equations

Charge on a mole of electrons (faraday)

Maximum work from an electrochemical cell

Relationship between Δ G ° and Δ E °

Relationship between Δ G ° and K for a redox reaction

Relationship between Δ E ° and K for a redox reaction at 25°C

Relationship between Δ G ° and Q

Relationship between E cell and Q at 25°C

19.5 Commercial Galvanic Cells

Learning Objective

1. To learn how commercial galvanic cells work.

Because galvanic cells can be self-contained and portable, they can be used as

batteries and fuel cells. A battery (storage cell)A galvanic cell (or series of galvanic

cells) that contains all the reactants needed to produce electricity. is a galvanic cell (or

a series of galvanic cells) that contains all the reactants needed to produce electricity.

In contrast, a fuel cellA galvanic cell that requires a constant external supply of one or

more reactants to generate electricity. is a galvanic cell that requires a constant

external supply of one or more reactants to generate electricity. In this section, we

describe the chemistry behind some of the more common types of batteries and fuel

cells.

Batteries

There are two basic kinds of batteries: disposable, or primary, batteries, in which the

electrode reactions are effectively irreversible and which cannot be recharged; and

rechargeable, or secondary, batteries, which form an insoluble product that adheres to

the electrodes. These batteries can be recharged by applying an electrical potential in

the reverse direction. The recharging process temporarily converts a rechargeable

battery from a galvanic cell to an electrolytic cell.

Batteries are cleverly engineered devices that are based on the same fundamental laws

as galvanic cells. The major difference between batteries and the galvanic cells we

have previously described is that commercial batteries use solids or pastes rather than

solutions as reactants to maximize the electrical output per unit mass. The use of

highly concentrated or solid reactants has another beneficial effect: the concentrations

of the reactants and the products do not change greatly as the battery is discharged;

consequently, the output voltage remains remarkably constant during the discharge

process. This behavior is in contrast to that of the Zn/Cu cell, whose output decreases

logarithmically as the reaction proceeds. When a battery consists of more than one

galvanic cell, the cells are usually connected in series—that is, with the positive (+)

terminal of one cell connected to the negative (−) terminal of the next, and so forth.

The overall voltage of the battery is therefore the sum of the voltages of the individual

cells.

Leclanché Dry Cell

The dry cell, by far the most common type of battery, is used in flashlights, electronic

devices such as the Walkman and Game Boy, and many other devices. Although the dry

cell was patented in 1866 by the French chemist Georges Leclanché and more than 5

billion such cells are sold every year, the details of its electrode chemistry are still not

completely understood. In spite of its name, the Leclanché dry cellA battery consisting

of an electrolyte that is an acidic water-based paste containing graphite, and starch. is

actually a “wet cell”: the electrolyte is an acidic water-based paste containing MnO2,

NH4Cl, ZnCl2, graphite, and starch (part (a) in the Figure below). The half-reactions at

the anode and the cathode can be summarized as follows:



The Zn2+ ions formed by the oxidation of Zn(s) at the anode react with NH3 formed at

the cathode and Cl− ions present in solution, so the overall cell reaction is as follows:


The dry cell produces about 1.55 V and is inexpensive to manufacture. It is not,

however, very efficient in producing electrical energy because only the relatively small




fraction of the MnO2 that is near the cathode is actually reduced and only a small

fraction of the zinc cathode is actually consumed as the cell discharges. In addition,

dry cells have a limited shelf life because the Zn anode reacts spontaneously with

NH4Cl in the electrolyte, causing the case to corrode and allowing the contents to leak

out.

The alkaline batteryA battery that consists of a Leclanché cell adapted to operate

under alkaline (basic) conditions. is essentially a Leclanché cell adapted to operate

under alkaline, or basic, conditions. The half-reactions that occur in an alkaline battery

are as follows:




This battery also produces about 1.5 V, but it has a longer shelf life and more constant

output voltage as the cell is discharged than the Leclanché dry cell. Although the

alkaline battery is more expensive to produce than the Leclanché dry cell, the

improved performance makes this battery more cost-effective.

Button Batteries

Although some of the small button batteries used to power watches, calculators, and

cameras are miniature alkaline cells, most are based on a completely different

chemistry. In these batteries, the anode is a zinc–mercury amalgam rather than pure




zinc, and the cathode uses either HgO or Ag2O as the oxidant rather than MnO2 (part

(b) in the Figure below). The cathode and overall reactions and cell output for these

two types of button batteries are as follows:





The major advantages of the mercury and silver cells are their reliability and their high

output-to-mass ratio. These factors make them ideal for applications where small size

is crucial, as in cameras and hearing aids. The disadvantages are the expense and the

environmental problems caused by the disposal of heavy metals, such as Hg and Ag.

Lithium–Iodine Battery

None of the batteries described above is actually “dry.” They all contain small amounts

of liquid water, which adds significant mass and causes potential corrosion problems.

Consequently, substantial effort has been expended to develop water-free batteries.

One of the few commercially successful water-free batteries is the lithium–iodine

batteryA battery that consists of an anode of lithium metal and a cathode containing a





solid complex of with a layer of solid LiI in between that allows the diffusion of ions..

The anode is lithium metal, and the cathode is a solid complex of I2. Separating them is

a layer of solid LiI, which acts as the electrolyte by allowing the diffusion of Li+ ions.

The electrode reactions are as follows:




http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0m/section_23/ad96c6b58f46a41eb574d4b699b2c5a5.jpg

Cardiac pacemaker. An x-ray of a patient showing the location and size of a pacemaker

powered by a lithium–iodine battery.

As shown in part (c) in the Figure below, a typical lithium–iodine battery consists of

two cells separated by a nickel metal mesh that collects charge from the anode.

Because of the high internal resistance caused by the solid electrolyte, only a low

current can be drawn. Nonetheless, such batteries have proven to be long-lived (up to






10 yr) and reliable. They are therefore used in applications where frequent

replacement is difficult or undesirable, such as in cardiac pacemakers and other

medical implants and in computers for memory protection. These batteries are also

used in security transmitters and smoke alarms. Other batteries based on lithium

anodes and solid electrolytes are under development, using TiS2, for example, for the

cathode.

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Figure: Three Kinds of Primary (Nonrechargeable) Batteries : (a) A Leclanché dry cell is

actually a “wet cell,” in which the electrolyte is an acidic water-based paste containing

MnO2, NH4Cl, ZnCl2, graphite, and starch. Though inexpensive to manufacture, the cell

is not very efficient in producing electrical energy and has a limited shelf life. (b) In a

button battery, the anode is a zinc–mercury amalgam, and the cathode can be either

HgO (shown here) or Ag2O as the oxidant. Button batteries are reliable and have a high

output-to-mass ratio, which allows them to be used in applications such as calculators

and watches, where their small size is crucial. (c) A lithium–iodine battery consists of

two cells separated by a metallic nickel mesh that collects charge from the anodes. The

anode is lithium metal, and the cathode is a solid complex of I2. The electrolyte is a

layer of solid LiI that allows Li+ ions to diffuse from the cathode to the anode. Although

this type of battery produces only a relatively small current, it is highly reliable and

long-lived.



Dry cells, button batteries, and lithium–iodine batteries are disposable and cannot be

recharged once they are discharged. Rechargeable batteries, in contrast, offer

significant economic and environmental advantages because they can be recharged

and discharged numerous times. As a result, manufacturing and disposal costs drop

dramatically for a given number of hours of battery usage. Two common rechargeable

batteries are the nickel–cadmium battery and the lead–acid battery, which we describe

next.

Nickel–Cadmium (NiCad) Battery

The nickel–cadmiumA type of battery that consists of a water-based cell with a

cadmium anode and a highly oxidized nickel cathode., or NiCad, battery is used in

small electrical appliances and devices like drills, portable vacuum cleaners, and

AM/FM digital tuners. It is a water-based cell with a cadmium anode and a highly

oxidized nickel cathode that is usually described as the nickel(III) oxo-hydroxide,

NiO(OH). As shown in the Figure below, the design maximizes the surface area of the

electrodes and minimizes the distance between them, which decreases internal

resistance and makes a rather high discharge current possible.

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Figure: The Nickel–Cadmium (NiCad) Battery, a Rechargeable Battery : NiCad

batteries contain a cadmium anode and a highly oxidized nickel cathode. This design

maximizes the surface area of the electrodes and minimizes the distance between

them, which gives the battery both a high discharge current and a high capacity.

The electrode reactions during the discharge of a NiCad battery are as follows:




Because the products of the discharge half-reactions are solids that adhere to the

electrodes [Cd(OH)2 and 2Ni(OH)2], the overall reaction is readily reversed when the

cell is recharged. Although NiCad cells are lightweight, rechargeable, and high

capacity, they have certain disadvantages. For example, they tend to lose capacity

quickly if not allowed to discharge fully before recharging, they do not store well for

long periods when fully charged, and they present significant environmental and

disposal problems because of the toxicity of cadmium.

A variation on the NiCad battery is the nickel–metal hydride battery (NiMH) used in

hybrid automobiles, wireless communication devices, and mobile computing. The

overall chemical equation for this type of battery is as follows:

NiO(OH)(s) + MH → Ni(OH)2(s) + M(s)






The NiMH battery has a 30%–40% improvement in capacity over the NiCad battery; it

is more environmentally friendly so storage, transportation, and disposal are not

subject to environmental control; and it is not as sensitive to recharging memory. It is,

however, subject to a 50% greater self-discharge rate, a limited service life, and higher

maintenance, and it is more expensive than the NiCad battery.

Lead–Acid (Lead Storage) Battery

The lead–acid batteryA battery consisting of a plate or grid of spongy lead metal, a

cathode containing powdered and an electrolyte that is usually an aqueous solution of

is used to provide the starting power in virtually every automobile and marine engine

on the market. Marine and car batteries typically consist of multiple cells connected in

series. The total voltage generated by the battery is the potential per cell (E°cell) times

the number of cells. As shown in the Figure below, the anode of each cell in a lead

storage battery is a plate or grid of spongy lead metal, and the cathode is a similar grid

containing powdered lead dioxide (PbO2). The electrolyte is usually an approximately

37% solution (by mass) of sulfuric acid in water, with a density of 1.28 g/mL (about 4.5

M H2SO4). Because the redox active species are solids, there is no need to separate the

electrodes. The electrode reactions in each cell during discharge are as follows:







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Figure: One Cell of a Lead–Acid Battery : The anodes in each cell of a rechargeable

battery are plates or grids of lead containing spongy lead metal, while the cathodes are

similar grids containing powdered lead dioxide (PbO2). The electrolyte is an aqueous

solution of sulfuric acid. The value of E° for such a cell is about 2 V. Connecting three

such cells in series produces a 6 V battery, whereas a typical 12 V car battery contains

six cells in series. When treated properly, this type of high-capacity battery can be

discharged and recharged many times over.

As the cell is discharged, a powder of PbSO4 forms on the electrodes. Moreover,

sulfuric acid is consumed and water is produced, decreasing the density of the

electrolyte and providing a convenient way of monitoring the status of a battery by

simply measuring the density of the electrolyte.



http://2012books.lardbucket.org/books/principles-of-general-chemistry-

Source: Photo courtesy of Mitchclanky2008,

http://www.flickr.com/photos/25597837@N05/2422765479/.

When an external voltage in excess of 2.04 V per cell is applied to a lead–acid battery,

the electrode reactions reverse, and PbSO4 is converted back to metallic lead and

PbO2. If the battery is recharged too vigorously, however, electrolysis of water can

occur, resulting in the evolution of potentially explosive hydrogen gas. The gas bubbles

formed in this way can dislodge some of the PbSO4 or PbO2 particles from the grids,

allowing them to fall to the bottom of the cell, where they can build up and cause an

internal short circuit. Thus the recharging process must be carefully monitored to

optimize the life of the battery. With proper care, however, a lead–acid battery can be

discharged and recharged thousands of times. In automobiles, the alternator supplies

the electric current that causes the discharge reaction to reverse.

Fuel Cells

A fuel cell is a galvanic cell that requires a constant external supply of reactants

because the products of the reaction are continuously removed. Unlike a battery, it

does not store chemical or electrical energy; a fuel cell allows electrical energy to be

extracted directly from a chemical reaction. In principle, this should be a more

efficient process than, for example, burning the fuel to drive an internal combustion

engine that turns a generator, which is typically less than 40% efficient, and in fact,

the efficiency of a fuel cell is generally between 40% and 60%. Unfortunately,

significant cost and reliability problems have hindered the wide-scale adoption of fuel

http://www.flickr.com/photos/25597837@N05/2422765479/

http://2012books.lardbucket.org/books/principles-of-general-chemistry-

cells. In practice, their use has been restricted to applications in which mass may be a

significant cost factor, such as US manned space vehicles.

These space vehicles use a hydrogen/oxygen fuel cell that requires a continuous input

of H2(g) and O2(g), as illustrated in the Figure below. The electrode reactions are as

follows:




http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0m/section_23/e26f9d07bec9214ec1f9209bf81bc1d0.jpg






Figure: A Hydrogen Fuel Cell Produces Electrical Energy Directly from a Chemical

Reaction: Hydrogen is oxidized to protons at the anode, and the electrons are

transferred through an external circuit to the cathode, where oxygen is reduced and

combines with H+ to form water. A solid electrolyte allows the protons to diffuse from

the anode to the cathode. Although fuel cells are an essentially pollution-free means of

obtaining electrical energy, their expense and technological complexity have thus far

limited their applications.

The overall reaction represents an essentially pollution-free conversion of hydrogen

and oxygen to water, which in space vehicles is then collected and used. Although this

type of fuel cell should produce 1.23 V under standard conditions, in practice the

device achieves only about 0.9 V. One of the major barriers to achieving greater

efficiency is the fact that the four-electron reduction of O2(g) at the cathode is

intrinsically rather slow, which limits current that can be achieved. All major

automobile manufacturers have major research programs involving fuel cells: one of

the most important goals is the development of a better catalyst for the reduction of

O2.

Summary

A battery is a contained unit that produces electricity, whereas a fuel cell is a galvanic

cell that requires a constant external supply of one or more reactants to generate

electricity. One type of battery is the Leclanché dry cell, which contains an electrolyte

in an acidic water-based paste. This battery is called an alkaline battery when adapted

to operate under alkaline conditions. Button batteries have a high output-to-mass ratio;

lithium–iodine batteries consist of a solid electrolyte; the nickel–cadmium (NiCad)

battery is rechargeable; and the lead–acid battery, which is also rechargeable, does

not require the electrodes to be in separate compartments. A fuel cell requires an

external supply of reactants as the products of the reaction are continuously removed.

In a fuel cell, energy is not stored; electrical energy is provided by a chemical reaction.

Key Takeaway

Commercial batteries are galvanic cells that use solids or pastes as reactants to

maximize the electrical output per unit mass.

19.6 Corrosion

Learning Objective

1. To understand the process of corrosion.

CorrosionA galvanic process by which metals deteriorate through oxidation—usually

but not always to their oxides. is a galvanic process by which metals deteriorate

through oxidation—usually but not always to their oxides. For example, when exposed

to air, iron rusts, silver tarnishes, and copper and brass acquire a bluish-green surface

called a patina. Of the various metals subject to corrosion, iron is by far the most

important commercially. An estimated $100 billion per year is spent in the United

States alone to replace iron-containing objects destroyed by corrosion. Consequently,

the development of methods for protecting metal surfaces from corrosion constitutes a

very active area of industrial research. In this section, we describe some of the

chemical and electrochemical processes responsible for corrosion. We also examine

the chemical basis for some common methods for preventing corrosion and treating

corroded metals.

Note the Pattern

Corrosion is a galvanic process.

Under ambient conditions, the oxidation of most metals is thermodynamically

spontaneous, with the notable exception of gold and platinum. Hence it is actually

somewhat surprising that any metals are useful at all in Earth’s moist, oxygen-rich

atmosphere. Some metals, however, are resistant to corrosion for kinetic reasons. For

example, aluminum in soft-drink cans and airplanes is protected by a thin coating of

metal oxide that forms on the surface of the metal and acts as an impenetrable barrier

that prevents further destruction. Aluminum cans also have a thin plastic layer to

prevent reaction of the oxide with acid in the soft drink. Chromium, magnesium, and

nickel also form protective oxide films. Stainless steels are remarkably resistant to

corrosion because they usually contain a significant proportion of chromium, nickel, or

both.

In contrast to these metals, when iron corrodes, it forms a red-brown hydrated metal

oxide (Fe2O3·xH2O), commonly known as rust, that does not provide a tight protective

film (Figure below). Instead, the rust continually flakes off to expose a fresh metal

surface vulnerable to reaction with oxygen and water. Because both oxygen and water

are required for rust to form, an iron nail immersed in deoxygenated water will not

rust—even over a period of several weeks. Similarly, a nail immersed in an organic

solvent such as kerosene or mineral oil saturated with oxygen will not rust because of

the absence of water.

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Figure: Rust, the Result of Corrosion of Metallic Iron : Iron is oxidized to Fe2+(aq) at an

anodic site on the surface of the iron, which is often an impurity or a lattice defect.

Oxygen is reduced to water at a different site on the surface of the iron, which acts as



the cathode. Electrons are transferred from the anode to the cathode through the

electrically conductive metal. Water is a solvent for the Fe2+ that is produced initially

and acts as a salt bridge. Rust (Fe2O3·xH2O) is formed by the subsequent oxidation of

Fe2+ by atmospheric oxygen.

In the corrosion process, iron metal acts as the anode in a galvanic cell and is oxidized

to Fe2+; oxygen is reduced to water at the cathode. The relevant reactions are as

follows:




The Fe2+ ions produced in the initial reaction are then oxidized by atmospheric oxygen

to produce the insoluble hydrated oxide containing Fe3+, as represented in the

following equation:


The sign and magnitude of E° for the corrosion process indicate that there is a strong

driving force for the oxidation of iron by O2 under standard conditions (1 M H+). Under

neutral conditions, the driving force is somewhat less but still appreciable (E = 1.25 V





at pH 7.0). Normally, the reaction of atmospheric CO2 with water to form H+ and

HCO3− provides a low enough pH to enhance the reaction rate, as does acid rain.

Automobile manufacturers spend a great deal of time and money developing paints

that adhere tightly to the car’s metal surface to prevent oxygenated water, acid, and

salt from coming into contact with the underlying metal. Unfortunately, even the best

paint is subject to scratching or denting, and the electrochemical nature of the

corrosion process means that two scratches relatively remote from each other can

operate together as anode and cathode, leading to sudden mechanical failure (Figure

below).

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Figure: Small Scratches in a Protective Paint Coating Can Lead to the Rapid Corrosion

of Iron: Holes in a protective coating allow oxygen to be reduced at the surface with

the greater exposure to air (the cathode), while metallic iron is oxidized to Fe2+(aq) at

the less exposed site (the anode). Rust is formed when Fe2+(aq) diffuses to a location

where it can react with atmospheric oxygen, which is often remote from the anode.

The electrochemical interaction between cathodic and anodic sites can cause a large



pit to form under a painted surface, eventually resulting in sudden failure with little

visible warning that corrosion has occurred.

One of the most common techniques used to prevent the corrosion of iron is applying a

protective coating of another metal that is more difficult to oxidize. Faucets and some

external parts of automobiles, for example, are often coated with a thin layer of

chromium using an electrolytic process. With the increased use of polymeric materials

in cars, however, the use of chrome-plated steel has diminished in recent years.

Similarly, the “tin cans” that hold soups and other foods are actually made of steel

coated with a thin layer of tin. Neither chromium nor tin is intrinsically resistant to

corrosion, but both form protective oxide coatings.

As with a protective paint, scratching a protective metal coating will allow corrosion to

occur. In this case, however, the presence of the second metal can actually increase

the rate of corrosion. The values of the standard electrode potentials for Sn2+ (E° =

−0.14 V) and Fe2+ (E° = −0.45 V) in Table: "Standard Potentials for Selected

Reduction Half-Reactions at 25°C" show that Fe is more easily oxidized than Sn. As a

result, the more corrosion-resistant metal (in this case, tin) accelerates the corrosion

of iron by acting as the cathode and providing a large surface area for the reduction of

oxygen (Figure below). This process is seen in some older homes where copper and

iron pipes have been directly connected to each other. The less easily oxidized copper

acts as the cathode, causing iron to dissolve rapidly near the connection and

occasionally resulting in a catastrophic plumbing failure.

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Figure: Galvanic Corrosion : If iron is in contact with a more corrosion-resistant metal

such as tin, copper, or lead, the other metal can act as a large cathode that greatly

increases the rate of reduction of oxygen. Because the reduction of oxygen is coupled

to the oxidation of iron, this can result in a dramatic increase in the rate at which iron

is oxidized at the anode. Galvanic corrosion is likely to occur whenever two dissimilar

metals are connected directly, allowing electrons to be transferred from one to the

other.

One way to avoid these problems is to use a more easily oxidized metal to protect iron

from corrosion. In this approach, called cathodic protection, a more reactive metal

such as Zn (E° = −0.76 V for Zn2+ + 2e− → Zn) becomes the anode, and iron becomes

the cathode. This prevents oxidation of the iron and protects the iron object from

corrosion. The reactions that occur under these conditions are as follows:







The more reactive metal reacts with oxygen and will eventually dissolve, “sacrificing”

itself to protect the iron object. Cathodic protection is the principle underlying

galvanized steel, which is steel protected by a thin layer of zinc. Galvanized steel is

used in objects ranging from nails to garbage cans. In a similar strategy, sacrificial

electrodesAn electrode containing a more reactive metal that is attached to a metal

object to inhibit that object’s corrosion. using magnesium, for example, are used to

protect underground tanks or pipes (Figure below). Replacing the sacrificial electrodes

is more cost-effective than replacing the iron objects they are protecting.

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Figure: The Use of a Sacrificial Electrode to Protect Against Corrosion : Connecting a

magnesium rod to an underground steel pipeline protects the pipeline from corrosion.





Because magnesium (E° = −2.37 V) is much more easily oxidized than iron (E° =

−0.45 V), the Mg rod acts as the anode in a galvanic cell. The pipeline is therefore

forced to act as the cathode at which oxygen is reduced. The soil between the anode

and the cathode acts as a salt bridge that completes the electrical circuit and

maintains electrical neutrality. As Mg(s) is oxidized to Mg2+ at the anode, anions in the

soil, such as nitrate, diffuse toward the anode to neutralize the positive charge.

Simultaneously, cations in the soil, such as H+ or NH4+, diffuse toward the cathode,

where they replenish the protons that are consumed as oxygen is reduced. A similar

strategy uses many miles of somewhat less reactive zinc wire to protect the Alaska oil

pipeline.

Summary

The deterioration of metals through oxidation is a galvanic process called corrosion.

Protective coatings consist of a second metal that is more difficult to oxidize than the

metal being protected. Alternatively, a more easily oxidized metal can be applied to a

metal surface, thus providing cathodic protection of the surface. A thin layer of zinc

protects galvanized steel. Sacrificial electrodes can also be attached to an object to

protect it.

Key Takeaway

Corrosion is a galvanic process that can be prevented using cathodic protection.

19.7 Electrolysis

Learning Objective

1. To understand electrolysis and describe it quantitatively.

In this chapter, we have described various galvanic cells in which a spontaneous

chemical reaction is used to generate electrical energy. In an electrolytic cell,

however, the opposite process, called electrolysisAn electrochemical process in which

an external voltage is applied to an electrolytic cell to drive a nonspontaneous

reaction., occurs: an external voltage is applied to drive a nonspontaneous reaction. In

this section, we look at how electrolytic cells are constructed and explore some of their

many commercial applications.

Note the Pattern

In an electrolytic cell, an external voltage is applied to drive a nonspontaneous

reaction.

Electrolytic Cells

If we construct an electrochemical cell in which one electrode is copper metal

immersed in a 1 M Cu2+ solution and the other electrode is cadmium metal immersed

in a 1 M Cd2+ solution and then close the circuit, the potential difference between the

two compartments will be 0.74 V. The cadmium electrode will begin to dissolve (Cd is

oxidized to Cd2+) and is the anode, while metallic copper will be deposited on the

copper electrode (Cu2+ is reduced to Cu), which is the cathode (part (a) in the Figure

below). The overall reaction is as follows:


This reaction is thermodynamically spontaneous as written (ΔG° < 0):


In this direction, the system is acting as a galvanic cell.



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Figure: An Applied Voltage Can Reverse the Flow of Electrons in a Galvanic Cd/Cu

Cell: (a) When compartments that contain a Cd electrode immersed in 1 M Cd2+(aq)

and a Cu electrode immersed in 1 M Cu2+(aq) are connected to create a galvanic cell,

Cd(s) is spontaneously oxidized to Cd2+(aq) at the anode, and Cu2+(aq) is spontaneously

reduced to Cu(s) at the cathode. The potential of the galvanic cell is 0.74 V. (b)

Applying an external potential greater than 0.74 V in the reverse direction forces

electrons to flow from the Cu electrode [which is now the anode, at which metallic

Cu(s) is oxidized to Cu2+(aq)] and into the Cd electrode [which is now the cathode, at

which Cd2+(aq) is reduced to Cd(s)]. The anode in an electrolytic cell is positive

because electrons are flowing from it, whereas the cathode is negative because

electrons are flowing into it.

The reverse reaction, the reduction of Cd2+ by Cu, is thermodynamically

nonspontaneous and will occur only with an input of 140 kJ. We can force the reaction

to proceed in the reverse direction by applying an electrical potential greater than

0.74 V from an external power supply. The applied voltage forces electrons through

the circuit in the reverse direction, converting a galvanic cell to an electrolytic cell.

Thus the copper electrode is now the anode (Cu is oxidized), and the cadmium



electrode is now the cathode (Cd2+ is reduced) (part (b) in the Figure above). The signs

of the cathode and the anode have switched to reflect the flow of electrons in the

circuit. The half-reactions that occur at the cathode and the anode are as follows:




Because E°cell < 0, the overall reaction—the reduction of Cd2+ by Cu—clearly cannot

occur spontaneously and proceeds only when sufficient electrical energy is applied.

The differences between galvanic and electrolytic cells are summarized in the Table

below.

Property Galvanic Cell Electrolytic Cell

ΔG < 0 > 0

E cell > 0 < 0

Electrode Process

anode oxidation oxidation

cathode reduction reduction

Sign of Electrode




Property Galvanic Cell Electrolytic Cell

anode − +

cathode + −

Table: Comparison of Galvanic and Electrolytic Cells

Electrolytic Reactions

At sufficiently high temperatures, ionic solids melt to form liquids that conduct

electricity extremely well due to the high concentrations of ions. If two inert electrodes

are inserted into molten NaCl, for example, and an electrical potential is applied, Cl− is

oxidized at the anode, and Na+ is reduced at the cathode. The overall reaction is as

follows:


This is the reverse of the formation of NaCl from its elements. The product of the

reduction reaction is liquid sodium because the melting point of sodium metal is

97.8°C, well below that of NaCl (801°C). Approximately 20,000 tons of sodium metal

are produced commercially in the United States each year by the electrolysis of molten

NaCl in a Downs cell (Figure below). In this specialized cell, CaCl2 (melting point =

772°C) is first added to the NaCl to lower the melting point of the mixture to about

600°C, thereby lowering operating costs.


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Figure: A Downs Cell for the Electrolysis of Molten NaCl : The electrolysis of a molten

mixture of NaCl and CaCl2 results in the formation of elemental sodium and chlorine

gas. Because sodium is a liquid under these conditions and liquid sodium is less dense

than molten sodium chloride, the sodium floats to the top of the melt and is collected in

concentric capped iron cylinders surrounding the cathode. Gaseous chlorine collects in

the inverted cone over the anode. An iron screen separating the cathode and anode

compartments ensures that the molten sodium and gaseous chlorine do not come into

contact.

Similarly, in the Hall–Heroult process used to produce aluminum commercially, a

molten mixture of about 5% aluminum oxide (Al2O3; melting point = 2054°C) and 95%

cryolite (Na3AlF6; melting point = 1012°C) is electrolyzed at about 1000°C, producing

molten aluminum at the cathode and CO2 gas at the carbon anode. The overall reaction

is as follows:





Oxide ions react with oxidized carbon at the anode, producing CO2(g).

There are two important points to make about these two commercial processes and

about the electrolysis of molten salts in general.

1. The electrode potentials for molten salts are likely to be very different from the

standard cell potentials listed in Table: "Standard Potentials for Selected

Reduction Half-Reactions at 25°C", which are compiled for the reduction of the

hydrated ions in aqueous solutions under standard conditions.

2. Using a mixed salt system means there is a possibility of competition between

different electrolytic reactions. When a mixture of NaCl and CaCl2 is

electrolyzed, Cl− is oxidized because it is the only anion present, but either Na+

or Ca2+ can be reduced. Conversely, in the Hall–Heroult process, only one cation

is present that can be reduced (Al3+), but there are three species that can be

oxidized: C, O2−, and F−.

In the Hall–Heroult process, C is oxidized instead of O2− or F− because oxygen and

fluorine are more electronegative than carbon, which means that C is a weaker oxidant

than either O2 or F2. Similarly, in the Downs cell, we might expect electrolysis of a

NaCl/CaCl2 mixture to produce calcium rather than sodium because Na is slightly less

electronegative than Ca (χ = 0.93 versus 1.00, respectively), making Na easier to

oxidize and, conversely, Na+ more difficult to reduce. In fact, the reduction of Na+ to

Na is the observed reaction. In cases where the electronegativities of two species are

similar, other factors, such as the formation of complex ions, become important and

may determine the outcome.

Electrolysis can also be used to drive the thermodynamically nonspontaneous

decomposition of water into its constituent elements: H2 and O2. However, because

pure water is a very poor electrical conductor, a small amount of an ionic solute (such



as H2SO4 or Na2SO4) must first be added to increase its electrical conductivity.

Inserting inert electrodes into the solution and applying a voltage between them will

result in the rapid evolution of bubbles of H2 and O2 (Figure below). The reactions that

occur are as follows:




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Figure: The Electrolysis of Water : Applying an external potential of about 1.7–1.9 V to

two inert electrodes immersed in an aqueous solution of an electrolyte such as H2SO4






or Na2SO4 drives the thermodynamically nonspontaneous decomposition of water into

H2 at the cathode and O2 at the anode.

For a system that contains an electrolyte such as Na2SO4, which has a negligible effect

on the ionization equilibrium of liquid water, the pH of the solution will be 7.00 and

[H+] = [OH−] = 1.0 × 10−7. Assuming that PO2 = PH2 = 1 atm, we can use the standard

potentials and the standard cell potential Equation to calculate E for the overall

reaction:


Thus Ecell is −1.23 V, which is the value of E°cell if the reaction is carried out in the

presence of 1 M H+ rather than at pH 7.0.

In practice, a voltage about 0.4–0.6 V greater than the calculated value is needed to

electrolyze water. This added voltage, called an overvoltageThe voltage that must be

applied in electrolysis in addition to the calculated (theoretical) value to overcome

factors such as a high activation energy and the formation of bubbles on a surface.,

represents the additional driving force required to overcome barriers such as the large

activation energy for the formation of a gas at a metal surface. Overvoltages are

needed in all electrolytic processes, which explain why, for example, approximately 14

V must be applied to recharge the 12 V battery in your car.

In general, any metal that does not react readily with water to produce hydrogen can

be produced by the electrolytic reduction of an aqueous solution that contains the

metal cation. The p-block metals and most of the transition metals are in this category,


but metals in high oxidation states, which form oxoanions, cannot be reduced to the

metal by simple electrolysis. Active metals, such as aluminum and those of groups 1

and 2, react so readily with water that they can be prepared only by the electrolysis of

molten salts. Similarly, any nonmetallic element that does not readily oxidize water to

O2 can be prepared by the electrolytic oxidation of an aqueous solution that contains

an appropriate anion. In practice, among the nonmetals, only F2 cannot be prepared

using this method. Oxoanions of nonmetals in their highest oxidation states, such as

NO3−, SO4

2−, PO43−, are usually difficult to reduce electrochemically and usually behave

like spectator ions that remain in solution during electrolysis.

Note the Pattern

In general, any metal that does not react readily with water to produce hydrogen can

be produced by the electrolytic reduction of an aqueous solution that contains the

metal cation.

Electroplating

In a process called electroplatingA process in which a layer of a second metal is

deposited on the metal electrode that acts as the cathode during electrolysis., a layer

of a second metal is deposited on the metal electrode that acts as the cathode during

electrolysis. Electroplating is used to enhance the appearance of metal objects and

protect them from corrosion. Examples of electroplating include the chromium layer

found on many bathroom fixtures or (in earlier days) on the bumpers and hubcaps of

cars, as well as the thin layer of precious metal that coats silver-plated dinnerware or

jewelry. In all cases, the basic concept is the same. A schematic view of an apparatus

for electroplating silverware and a photograph of a commercial electroplating cell are

shown in the Figure below.

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Figure: Electroplating : (a) Electroplating uses an electrolytic cell in which the object to

be plated, such as a fork, is immersed in a solution of the metal to be deposited. The

object being plated acts as the cathode, on which the desired metal is deposited in a

thin layer, while the anode usually consists of the metal that is being deposited (in this

case, silver) that maintains the solution concentration as it dissolves. (b) In this

commercial electroplating apparatus, a large number of objects can be plated

simultaneously by lowering the rack into the Ag+ solution and applying the correct

potential.

The half-reactions in electroplating a fork, for example, with silver are as follows:







The overall reaction is the transfer of silver metal from one electrode (a silver bar

acting as the anode) to another (a fork acting as the cathode). Because E°cell = 0 V, it

takes only a small applied voltage to drive the electroplating process. In practice,

various other substances may be added to the plating solution to control its electrical

conductivity and regulate the concentration of free metal ions, thus ensuring a smooth,

even coating.

Quantitative Considerations

If we know the stoichiometry of an electrolysis reaction, the amount of current passed,

and the length of time, we can calculate the amount of material consumed or produced

in a reaction. Conversely, we can use stoichiometry to determine the combination of

current and time needed to produce a given amount of material.

The quantity of material that is oxidized or reduced at an electrode during an

electrochemical reaction is determined by the stoichiometry of the reaction and the

amount of charge that is transferred. For example, in the reaction Ag+(aq) + e− →

Ag(s), 1 mol of electrons reduces 1 mol of Ag+ to Ag metal. In contrast, in the reaction

Cu2+(aq) + 2e− → Cu(s), 1 mol of electrons reduces only 0.5 mol of Cu2+ to Cu metal.

Recall that the charge on 1 mol of electrons is 1 faraday (1 F), which is equal to 96,486

C. We can therefore calculate the number of moles of electrons transferred when a

known current is passed through a cell for a given period of time. The total charge (C)

transferred is the product of the current (A) and the time (t, in seconds):


The stoichiometry of the reaction and the total charge transferred enable us to

calculate the amount of product formed during an electrolysis reaction or the amount

of metal deposited in an electroplating process.


For example, if a current of 0.60 A passes through an aqueous solution of CuSO4 for

6.0 min, the total number of coulombs of charge that passes through the cell is as

follows:


The number of moles of electrons transferred to Cu2+ is therefore


Because two electrons are required to reduce a single Cu2+ ion, the total number of

moles of Cu produced is half the number of moles of electrons transferred, or

1.2 × 10−3 mol. This corresponds to 76 mg of Cu. In commercial electrorefining

processes, much higher currents (greater than or equal to 50,000 A) are used,

corresponding to approximately 0.5 F/s, and reaction times are on the order of 3–4

weeks.

Summary

In electrolysis, an external voltage is applied to drive a nonspontaneous reaction. A

Downs cell is used to produce sodium metal from a mixture of salts, and the Hall–

Heroult process is used to produce aluminum commercially. Electrolysis can also be

used to produce H2 and O2 from water. In practice, an additional voltage, called an

overvoltage, must be applied to overcome factors such as a large activation energy and

a junction potential. Electroplating is the process by which a second metal is deposited

on a metal surface, thereby enhancing an object’s appearance or providing protection



from corrosion. The amount of material consumed or produced in a reaction can be

calculated from the stoichiometry of an electrolysis reaction, the amount of current

passed, and the duration of the electrolytic reaction.

Key Takeaways

In electrolysis, an external voltage is applied to drive a nonspontaneous

reaction.

The quantity of material oxidized or reduced can be calculated from the

stoichiometry of the reaction and the amount of charge transferred.

Key Equation

Relationship of charge, current and time

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